Gabriela is 32 years older than Luis. Eight years ago, Gabriela was 5 times as old as Luis. How old is Luis now?
Solution: We can use the given information to write down two equations that describe the ages of Gabriela and Luis. Let Gabriela's current age be $g$ and Luis's current age be $l$ The information in the first sentence can be expressed in the following equation: $g = l + 32$ Eight years ago, Gabriela was $g - 8$ years old, and Luis was $l - 8$ years old. The information in the second sentence can be expressed in the following equation: $g - 8 = 5(l - 8)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $l$ , it might be easiest to use our first equation for $g$ and substitute it into our second equation. Our first equation is: $g = l + 32$ . Substituting this into our second equation, we get the equation: $(l + 32)$ $-$ $8 = 5(l - 8)$ which combines the information about $l$ from both of our original equations. Simplifying both sides of this equation, we get: $l + 24 = 5 l - 40$ Solving for $l$ , we get: $4 l = 64$ $l = 16$.